W6 Partial Homework
1 . Individual Problems 15-1
Mr. Ward and Mrs. Ward typically vote oppositely in elections, so their votes “cancel each other out.” They each gain 10 units of utility from a vote for their positions (and lose 10 units of utility from a vote against their positions). However, the bother of actually voting costs each 5 units of utility. The following matrix summarizes the strategies for both Mr. Ward and Mrs. Ward.
Using the given information, fill in the payoffs for each cell in the matrix. For example, in the top left cell, fill in the payoffs for Mr. Ward and Mrs. Ward if they both vote. (Hint: Be sure to enter a minus sign if the payoff is negative.)
| Mrs. Ward | |||
| Vote | Don’t Vote | ||
| Mr. Ward | Vote | Mr. Ward:
, Mrs. Ward
|
Mr. Ward:
, Mrs. Ward
|
| Don’t Vote | Mr. Ward:
, Mrs. Ward
|
Mr. Ward:
, Mrs. Ward
|
5 . Individual Problems 15-5
Every year, management and labor renegotiate a new employment contract by sending their proposals to an arbitrator, who chooses the best proposal (effectively giving one side or the other $5 million). Each side can choose to hire, or not hire, an expensive labor lawyer (at a cost of $200,000) who is effective at preparing the proposal in the best light. If neither hires a lawyer or if both hire lawyers, each side can expect to win about half the time. If only one side hires a lawyer, it can expect to win three fourth, or 0.75, of the time.
Use the given information to fill in the expected payoff, in dollars, for each cell in the matrix. (Hint: To find the expected payoff, multiply the probability of winning by the dollar amount of the payoff. Be sure to account for lawyer costs, which are incurred with certainty if a lawyer is hired.)
| Management (M) | |||
| No Lawyer | Lawyer | ||
| Labor (L) | No Lawyer | L:
, M:
|
L:
, M:
|
| Lawyer | L:
, M:
|
L:
, M:
|
The Nash equilibrium for this game is for Management to hire / not hire a lawyer, and for Labor to hire / not hire a lawyer.
7 . Individual Problems 16-1
Two equal-sized newspapers have an overlap circulation of 10% (10% of the subscribers subscribe to both newspapers). Advertisers are willing to pay $23 to advertise in one newspaper but only $44 to advertise in both, because they’re unwilling to pay twice to reach the same subscriber. Suppose the advertisers bargain by telling each newspaper that they’re going to reach agreement with the other newspaper, whereby they pay the other newspaper $21 to advertise.
According to the nonstrategic view of bargaining, each newspaper would earn
of the $21 in value added by reaching an agreement with the advertisers. The total gain for the two newspapers from reaching an agreement is
.
Suppose the two newspapers merge. As such, the advertisers can no longer bargain by telling each newspaper that they’re going to reach agreement with the other newspaper. Thus, the total gains for the two parties (the advertisers and the merged newspapers) from reaching an agreement with the advertisers are $21.
According to the nonstrategic view of bargaining, each merged newspaper will earn
in an agreement with the advertisers. This gain to the merged newspaper is greater / less than the total gains to the individual newspapers pre-meger.
11 . Individual Problems 16-5
Your pharmaceutical firm is seeking to open up new international markets by partnering with various local distributors. The different distributors within a country are stronger with different market segments (hospitals, retail pharmacies, etc.) but also have substantial overlap.
In Egypt, you calculate that the annual value created by one distributor is $330 million per year, but would be $440 million if two distributors carried your product line.
Assuming a nonstrategic view of bargaining, you would expect to capture
million of this deal. (Hint: The two distributors are independent of each other; therefore, you conduct separate negotiations with each.)
Argentina also has two distributors that add value equivalent to the value added by the two distributors in Egypt, but both are run by the government.
Assuming a nonstrategic view of bargaining, you would expect to capture
million of this deal.
In Argentina, if you do not reach an agreement with the government distributors, you can set up a less efficient Internet-based distribution system that would generate $110 million in value to you.
Assuming a nonstrategic view of bargaining, you would expect to capture
million of this deal.
12 . Individual Problems 16-6
Pharmaceutical Benefits Managers (PBMs) are intermediaries between upstream drug manufacturers and downstream insurance companies. They design formularies (lists of drugs that insurance will cover) and negotiate prices with drug companies. PBMs want a wider variety of drugs available to their insured populations, but at low prices. Suppose that a PBM is negotiating with the makers of two nondrowsy allergy drugs, Claritin and Allegra, for inclusion on the formulary. The “value” or “surplus” created by including one nondrowsy allergy drug on the formulary is $232 million, but the value of adding a second drug is only $46 million.
Assume the PBM bargains by telling each drug company that it’s going to reach an agreement with the other drug company.
Under the non-strategic view of bargaining, the PBM would earn a surplus of
million, while each drug company would earn a surplus of
million.
Now suppose the two drug companies merge. What is the likely postmerger bargaining outcome?
Under the nonstrategic view of bargaining, the PBM would earn a surplus of
million, while the merged drug company would earn a surplus of
million.
13 . Individual Problems 17-1
Malaysia
You’re the manager of global opportunities for a U.S. manufacturer that is considering expanding sales into Asia. Your market research has identified the market potential in Malaysia, the Philippines, and Singapore as described in the following table:
| Success Level | |||
| Big | Mediocre | Failure | |
| Malaysia | |||
| Probability | 0.7 | 0.1 | 0.2 |
| Units | 1,300,000 | 416,000 | 0 |
| Philippines | |||
| Probability | 0.2 | 0.3 | 0.5 |
| Units | 600,000 | 360,000 | 0 |
| Singapore | |||
| Probability | 0.4 | 0.3 | 0.3 |
| Units | 1,500,000 | 750,000 | 0 |
The product sells for $20, and each unit has a constant marginal cost of $16. Assume that the (fixed) cost of entering the market (regardless of which market you select) is $500,000.
In the following table, enter the expected number of units sold, and the expected profit, from entering each market.
| Market | Expected Number of Units Sold | Expected Profit |
| Malaysia | ||
| Philippines | ||
| Singapore |
If you were to enter one of the previously described markets, which one would you enter in order to earn the highest expected profit?
Philippines
Singapore
Malaysia
14 . Individual Problems 17-2
You’re a contestant on a TV game show. In the final round of the game, if contestants answer a question correctly, they will increase their current winnings of $3 million to $4 million. If they are wrong, their prize is decreased to $2,250,000. You believe you have a 25% chance of answering the question correctly.
Ignoring your current winnings, your expected payoff from playing the final round of the game show is
. Given that this is negative / positive , you should / should not play the final round of the game. (Hint: Enter a negative sign if the expected payoff is negative.)
The lowest probability of a correct guess that would make the guessing in the final round profitable (in expected value) is 34.2857% , 42.8571% , 42.4286% , 45.0000% . (Hint: At what probability does playing the final round yield an expected value of zero?)
15.
The residential division of Prism’s high-speed Internet service uses one advertising agency, while its commercial division uses another. Two analysts, Andy and Brad, are asked to test the effectiveness of the two agencies. Andy proposes an A/B test that compares the click-through rates per ad of the two agencies. Brad proposes a difference-in-difference test in which the budgets for both agencies are increased by 50%, and the percentage changes in the click-through rates are compared.
True or False: Brad’s difference-in-differences estimator is more likely to suffer from “leakage” than Andy’s.
True
False
16 . Individual Problems 17-4
Your company has a customer who is shutting down a production line, and it is your responsibility to dispose of the extrusion machine. The company could keep it in inventory for a possible future product and estimates that the reservation value is $150,000. Your dealings on the secondhand market lead you to believe that if you commit to a price of $200,000, there is a 0.5 chance you will be able to sell the machine. If you commit to a price of $250,000, there is a 0.3 chance you will be able to sell the machine. If you commit to a price of $300,000, there is a 0.1 chance you will be able to sell the machine. These probabilities are summarized in the following table.
For each posted price, enter the expected value of attempting to sell the machine at that price. (Hint: Be sure to take into account the value of the machine to your company in the event that you are not be able to sell the machine.)
| Posted Price | Probability of Sale | Expected Value |
| ($) | ($) | |
| $300,000 | 0.1 | |
| $250,000 | 0.3 | |
| $200,000 | 0.5 |
Assume you must commit to one posted price.
In order to maximize the expected profit of the potential sale, which posted price would you commit to in order to maximize the expected value of the potential sale of the machine?
$200,000
$250,000
$300,000
17 . Individual Problems 17-5
You are offered the following gamble based on coin flips. If the first heads occurs on the first flip, you get $2. If the first heads occurs on the second flip, you get $4, and so on, so that if the first heads is on the Nth flip, you get $2N
. The game continues until there is a heads.
Which of the following best represents the expected value of this gamble in dollars?
0
e
π
∞
When offered, most people say they would pay only less than $10 to play this game.
One explanation for this phenomenon is that individuals ignore / account for very unlikely events when making decisions.
18 . Individual Problems 17-6
The HR department is trying to fill a vacant position for a job with a small talent pool. Valid applications arrive every week or so, and the applicants all seem to bring different levels of expertise. For each applicant, the HR manager gathers information by trying to verify various claims on the candidate’s résumé, but some doubt about “fit” always lingers when a decision to hire or not is to be made.
Suppose that hiring an employee who is a bad fit for the company results in an error cost of $900, but failing to hire a good employee results in an error cost of $200 to the company. Although it is impossible to tell in advance whether an employee is a good fit, assume that the probability that an applicant is a “good fit” is 0.4, while the probability that an applicant is a “bad fit” is 1−0.4=0.6
. Hiring an applicant who is a good fit, as well as not hiring an applicant who is a bad fit, results in no error cost to the company.
For each decision in the following table, calculate and enter the expected error cost of that decision.
| Decision | Reality | Expected Error Cost | |
| Good Fit | Bad Fit | ||
| p=0.4 | p=0.6 | ||
| Hire | Cost: 0 | Cost: $900 | |
| Do Not Hire | Cost: $200 | Cost: 0 |
Suppose an otherwise qualified applicant applies for a job.
In order to minimize expected error costs, the HR department should hire / not hire the applicant.